1. Dr. Cynthia Furse University of Utah
Introduction to Electrical & Computer Engineering Digital Circuits – Very Brief Introduction
Dr. Cynthia Furse
University of Utah

2. Digital Circuits – Brief Intro
Analog & Digital
Binary (Digital) Numbers & Binary Math
Computers & Binary
Digital Logic Gates
NOT OR XOR AND NAND
Hooking up Digital Circuits

3. Digital vs. Analog
Digital is fixed (can take one or a few values, something you can count)
Analog varies (can take any value, something you can measure)

4. Analog vs. Digital – Fuel Gauge
Analog Gauge tells you ‘how much’ fuel you have
Digital Light tells you you have enough (off) or you don’t (on)

5. Analog vs. Digital – Clocks
Analog Clock tells you ‘what time it is’ (continuous)
Digital clock tells you what hour and minute it is (countable)

6. Dr. Thomas Stockham University of Utah
Analog opera recordings have distortion
Digital Recording lets you remove distortion

7. Analog vs. Digital – Voltmeters
Analog Voltmeter tells you ‘what voltage it is’ (continuous)
Digital voltmeter tells you voltage to xx.xx digits (countable)
OR just ‘on’ and ‘off’

8. Analog vs. Digital – Voltages
Analog Voltage can be ‘any value’ (Dimmer Switch)
Digital voltage is a limited set of voltages On =1 OR Off = 0

9. Analog vs. Digital – Voltages
Analog Voltage can be ‘any value’
Digital voltage is a limited set of voltages (Stairstepped)

10. Digital – Represent with Binary #s

11. Analog to Digital Conversion (ADC) Digital to Analog Conversion (DAC)
Analog Voltage can be ‘any value’
Digital voltage is a limited set of voltages – Quantization Error

12. Counting with Binary #s
000 = 0
001 = 1
010 = 2
011 = 3
100 = 4
101 = 5
110 = 6
111 = 7

13. Bits & Bytes
<< 8 BITS = 1 Byte

14. Computer Numbers
Computers represent numbers as a set of bits (8,16,32 bit) & an exponent 2000 = 2 x 10^ = = 3

15. Computers Represent Letters with ASCII codes
A = = ‘41’ a = = ‘61’
B = = ‘42’ b = = ‘62’
C = = ‘43’ c = = ‘63’
D = = ‘44’ d = = ‘64’
Etc.

16. Write your name in ASCII I R B J S C K T D L U E M V F N W G O X H P Y Q Z

17. How Computers Represent Pictures Pixel (eg. DPI = Dots per inch)
Digital (pixels) Analog (? Or just more pixels)

18. How Computers Represent Pictures Color: Red + Green + Blue (RGB)
Wikipedia

19. Computer Logic: 5V = ‘1’ = ‘on’ = ‘yes’ = ‘true’
0V = ‘0’ = ‘Off’ = ‘no’ = ‘false’

20. Example: Battery Voltage Sensing
A battery is considered low when its voltage is under 1.3V
Battery 1 Battery 2

21. Example: Is the Battery Charged?
ECE-speak: Is the battery voltage above 1.3V?
Convert voltage to digital (0 or 5)
Battery voltage Vb
=5V
= A(Vb-1.3V)
1.3V 0V
=5V = ‘1’
0V = ‘0’

22. Example: Are BOTH Batteries Charged?
Are Vo1 AND Vo2 both ‘1’?
AND

23. Example: Is at least one of the Batteries Charged?
Is either Vo1 OR Vo2 ‘1’? OR

24. Example: Does at least one of the batteries need to be charged?
Is at least one of Vo1 AND Vo2 ‘0’?
NAND

25. Others
Excusive-OR (XOR)
NOT

26. Building with Logic Gates
AND
GND
Remember the Power Supply Voltages! 5V

27. Digital Circuits – Brief Intro
Analog & Digital
Binary (Digital) Numbers & Binary Math
Computers & Digital
Digital Logic Gates
NOT OR XOR AND NAND
Hooking up Digital Circuits

28. Tombstone Rock near Moab, Utah